On the other hand, deep clustering involves simultaneously learning cluster assignments and features using deep neural networks. Simultaneously learning the feature spaces with a clustering objective in deep clustering may lead to degenerate solutions, which until recently limited end-to-end implementations of clustering with representation learning approaches [1]}. Subsequently, there have been several works [2]}, [1]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. We give details of some of these works in the Section REF . We categorize current clustering and representation learning works based on consistency constraints that are used to define the objective function of these works. We define an additional notion of consistency, consensus consistency, which ensures that representations are learnt to induce similar partitions for variations in the representation space, different clustering algorithms or different initializations of a clustering algorithm. We use consensus consistency and propose an end-to-end learning approach which outperforms other end-to-end learning methods for image clustering. We summarize our contributions as follows:
